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On the stability of the quadratic mapping in normed spaces

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  • Gwang Hui Kim

Abstract

The Hyers-Ulam stability, the Hyers-Ulam-Rassias stability, and also the stability in the spirit of Gavruţa for each of the following quadratic functional equations f ( x + y ) + f ( x − y ) = 2 f ( x ) + 2 f ( y ) , f ( x + y + z ) + f ( x − y ) + f ( y − z ) + f ( z − x ) = 3 f ( x ) + 3 f ( y ) + 3 f ( z ) , f ( x + y + z ) + f ( x ) + f ( y ) + f ( z ) = f ( x + y ) + f ( y + z ) + f ( z + x ) are investigated.

Suggested Citation

  • Gwang Hui Kim, 2001. "On the stability of the quadratic mapping in normed spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 25, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:358707
    DOI: 10.1155/S0161171201004707
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    Cited by:

    1. Sang Og Kim, 2020. "Stability of the Fréchet Equation in Quasi-Banach Spaces," Mathematics, MDPI, vol. 8(4), pages 1-20, April.

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